Fie b, c lungimile catetelor.
[tex]\it S_1=\dfrac{bc}{2}=24\Rightarrow bc=48\ \ \ \ (1)\\ \\ \\ S_2=\dfrac{(b-1)(c+3)}{2}=27,5 \Rightarrow (b-1)(c+3)=55 \Rightarrow\\ \\ \\ \Rightarrow bc+3b-c-3=55 \stackrel{(1)}{\Longrightarrow}\ 48+3b-c-3=55 \Rightarrow 3b-c=55+3-48 \Rightarrow\\ \\ \\ \Rightarrow 3b-c=10|_{\cdot c} \Rightarrow 3bc-c^2=10c \stackrel{(1)}{\Longrightarrow} 144=c^2+10c \Rightarrow c^2+10c-144=0\Rightarrow[/tex]
[tex]\it \Rightarrow c^2-8c+18c-144=0 \Rightarrow c(c-8) +18(c-8)=0 \Rightarrow\\ \\ \\ \Rightarrow(c-8)(c+18)=0 \Rightarrow \begin{cases}\it c-8=0 \Rightarrow c=8\\ \\ \it c+18=0 \Rightarrow c=-18(\ nu\ convine\ )\end{cases}\\ \\ \\ Prin\ urmare,\ c=8\ \ \ \ (2)\\ \\ \\ (1),(2) \Rightarrow b\cdot8=48 \Rightarrow b=6[/tex]
